"great for the chase" vs "expert in the chase"

"great man" is a noun.

In this context, "expert" is an adjective (some would say it's an adverb).

Compare:

Is John good at tennis?

He is an expert (in the game of tennis)

Here 'expert' is a noun.

Is John good at tennis?

He is expert (at the game of tennis)

Here 'expert' qualifies John's quality of playing.

EDIT

"A good man in X" is different from "A good man for X"

John is a good man in a difficult situation. (This mean that John is capable and you want to have him on your team when things get tough)

John is a good man for hunting. (This mean that John likes hunting and will always accept an invitation to go hunting)