Having given a hand was fully occupied (7)
I believe the answer is:
engaged
'fully occupied' is the definition.
(I've seen this before)
I don't understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for engaged that I've seen before include "Formally committed to marriage" , "Absorbed" , "Promised - book - fighting" , "Plighted; hired" , "Spoken for" .)