Little time to grasp an old, funny old instrument (8)
I believe the answer is:
mandolin
'old instrument' is the definition.
'little time to grasp an old funny' is the wordplay.
'little time' becomes 'min' (short for minute).
'to grasp' means one lot of letters goes inside another.
'funny' indicates an anagram.
'an'+'old'='anold'
'anold' is an anagram of 'andol'.
'min' placed around 'andol' is 'MANDOLIN'.
(Other definitions for mandolin that I've seen before include "Musical instrument like a small guitar" , "Stringed instrument, usually played with a plectrum" , "Instrument resembling a lute" , "'Captain Corelli's - - '" , "Lute-like instrument" .)