The Otago Peninsula Trust is seeking the money, over two years, for fencing native bush on the site, planting and spraying.
It has asked for $27,525 in the first year and $16,325 in the second.
The new fund, announced earlier this year, is for biodiversity projects on public land, but community groups rather than councils may apply for the $4 million which is to be allocated over two years.
The Dunedin City Council bought the 328ha block earlier this year for $2.6 million to preserve its heritage, biodiversity and geographic values.
Trust chairman John Jillett said the work would probably include trying to amalgamate existing pockets of native vegetation with extra planting.
Trust general manager Robyn McDonald said she had no indication when a decision might be made on the application, and added it would be "fantastic" if the funding were forthcoming.
This week Task Force Green workers are expected to be in action installing marker posts for three tracks on the property ready for walkers to visit the area over the summer break.
Cr Dave Cull, chairman of the Harbour Cone Steering Group, which is looking at the future uses of the block, said marking of the tracks should be completed before Christmas.
The tracks will not be gravelled because of the look and the cost of maintenance and the number of marker posts will also be kept to a minimum to preserve the existing appearance of the area as much as possible.
Cr Cull said one of the tracks, which finishes about three quarters of the way up Harbour Cone, would be "extremely good for people wanting to lose weight".
Another one which runs along an old benched car track from the top of Camp St in Broad Bay was virtually flat, however.
Users of the tracks will be asked not to disturb heritage sites, which will eventually be marked with signs and information.
A plan showing where the tracks will be is expected to be released soon.
Consultation has also begun over a possum eradication plan being organised through the Otago Peninsula Biodiversity Group, which has been allocated $35,000 from the Department of Conservation, along with $4000 from other peninsula groups.
It is hoped an eradication plan will be implemented late next year.
