It might be possible to design and synthesize a transition state analog inhibitor or a non-cleavable substrate analog inhibitor of the protease based on the known cleavage site, attach this to a solid support, and use the resulting affinity resin to pull down the protease from a cellular extract containing it. Mass spec sequencing of the bound protein could then be used to identify it.

Make a fluorescent substrate based on the known cleavage site, then use the substrate to screen crude and fractionated samples from a source that contains the protease.

To conduct the above said experiments you need to know exactly which inhibitor will bind.

Check out if its a inhibited by synthetic inhibitors for cysteine (E-64, IAA), serine (PMSF, TPCK, TLCK, and elastatinal), metalo (EDTA) or aspartic (pepstatin) proteases.

I agree with all answers above.