I'd like to make a fresh fig gelatin, but of course the proteases in fig make this difficult. If I make an agar clarification of the fresh fig puree, will the proteases be removed?
So, there are 2 problems with the possible solution of agar clarification:
1) Agar clarification (as far as I know) does involve heat to melt the agar and keep it melted - and usually you dissolve the agar IN the juice without any solvent, so, if you're going to heat up your juice enough for it to clarify, you're going to heat it up enough to break the proteases down. Bottom line, just boil the juice for the proteins to denaturate and save the money from the agar.
2) Proteases are very small protein chains and are unlikely to be completely removed by agar clarification. This process works because the agar "drags" the large molecules (like cellulose, etc.) and solids from the juice during the solidification process. You might remove some of the ficin, but not much. Also, issue #1 makes this answer redundant if you're not liking the idea of boiling your fruit...
Although, since your objective is to make some kind of solid from the fruit puree, why don't you use the agar itself to make the gel? You can use a small portion of the fruit juice/puree and then add the remainder later.