That depends.

If recluse is an adjective, then it would be

deliberately (adverb) recluse (adjective) = same as = deliberately reclusive

If recluse is a noun, then it would be:

deliberate (adjective) recluse (noun)

Note that recluse may be both, depending on context. In your context I'd say it's a noun, therefore the original sentence is correct.

That depends.

If recluse is an adjective, then it would be

deliberately (adverb) recluse (adjective, rare) = same as = deliberately reclusive

If recluse is a noun, then it would be:

deliberate (adjective) recluse (noun)

Note that recluse may be both, depending on context, although recluse as an adjective is very rarely used today. In your context I'd say it's a noun, therefore the original sentence is correct.