Both invite talk of reform: for global governance; and to secure social and political stability.
First the UN.
Anyone meeting the shy, serious young Miss Clark four and a-half decades back would have needed deep insight and/or an expansive imagination to project her trajectory.
She battled Labour's governing misogynists to reach the party executive, then Parliament, then (after the Rogergnomes blacklisted her from the 1984-87 cabinet) Deputy Prime Minister in 1989 when Sir Geoffrey Palmer succeeded David Lange.
Miss Clark engineered Mike Moore's 1990 takeover from Sir Geoffrey, pondered leaving politics in mid-1993 but steeled up to dump Mr Moore in December, faced down a coup in mid-1996, learnt about lipstick and hairdos and pulled Labour out of the ditch in the 1996 election.
She was nine years prime minister.
She ran a tight ship envious critics called ‘‘Helengrad''.
She brought that to the UN Development Programme (UNDP) and would bring it to the UN as a whole (which would not be welcome to staffers from some countries who don't share Miss Clark's Presbyterian-upbringing work ethic).
Eastern Europe is claiming a turn at the top.
But illiberal regimes there boost Miss Clark's appeal to the three democratic permanent members of the Security Council, which makes the appointment - and, remember, she lined up powerful backers before going for the UNDP job.
A New York Times editorial on April 9 featured her photo alone.
Also, for the first time candidates will front the General Assembly.
So don't bet on Miss Clark not winning. But Miss Clark is not radical.
Nor have forces for radical reform built up.
Nation-state sovereignty, the UN's basis, is still alive, even if globalisation, the internet and new technologies have clipped wings and other tender parts.
Despite feints towards global governance, as in rules on intellectual property and war and the OECD's attempt to tighten tax administration, a transit from international to global is not imminent.
Miss Clark's reforms would be managerial (plus intelligent rhetoric).
As was her prime ministership: a version of the ‘‘third way'', adapting Labour's social democracy to globalised, marketised reality by making it more liveable for the less strong and less-well-off.
She did not set out to remake society.
Miss Clark's Labour did not worry about the ‘‘future of work'', as Andrew Little's Labour has to.
The fragmentation and uncertainty of work is compounded by the separation of the richest 1% and their elitist hangers-on from the rest who depend on that undependable, often poorly paid, work - a division highlighted by last week's Panama tax haven revelations.
Finance sector alumnus John Key blandly asserted New Zealand is not a tax haven.
But it is known to the 1%, and now to the taxpaying not-rich, as a soft-touch haven of some sort for tainted money.
Some firms here make tidy profits, an enterprise Mr Key extolled, though by yesterday he was talking of an inquiry.
The deep social change these factors reflect will in the next decade or two require deep reform.
Meantime, eruptive populist forces feeding on anger, frustration and distrust have eroded, and in some countries ended, the dominance in liberal democracies of the big, old parties spanning what used to be the ‘‘centre''.
Here in periods of deep social change in the past 100 years (the 1930s economic strain, the 1980s generational lurch), it was Labour that did the deep reforming.
National was the post-reform consolidator and manager.
Can Labour do it this time round?
Labour was built on and out of a social structure fashioned by the industrial revolution: organised wage workers and their sympathisers and allies. Allegiance to Labour was quasi-tribal.
Social groupings are differently arranged now: they are politically porous and their profiles change by generation.
Many grumpy wage workers have switched to Key (hence National's still strong polling) or Winston Peters.
Younger people are more likely to align with a ‘‘movement'' and then often transitorily.
The Greens, which originated as a ‘‘movement'' sort of party, are the nearest to that way of thinking.
In 2014, Kim Dotcom's Internet party claimed to be such a party.
Its name conjured the sort of social-media-centred activism and support that coalesced around Barack Obama in 2008 and is now much more loosely - wistfully? - floating around Bernie Sanders.
Labour has not wound them in.
That poses Labour an existential challenge.
Will it be able to match this round of social change with deep reforms that lock in a new generation? Will the Greens?
Or will the reform response come through some other channel?
In the 1890s, the Liberals were the deep reformers. By the 1930s they were a shell.
These are questions consolidator/manager Miss Clark as Labour leader neither countenanced nor needed to.
Mr Little and Co have no real choice.
● Colin James is a social and political commentator.
