Finish searching for a fathead in the back of beyond (4)
I believe the answer is:
find
'finish searching for' is the definition.
'find' can be an answer for 'finish' (finding is a kind of finishing). I'm not certain of the 'searching for' bit.
'a fathead in the back of beyond' is the wordplay.
'a fathead' becomes 'f' (head letter of 'fat').
'the back of' indicates one should take the final letters.
The last letter of 'beyond' is 'd'.
'f'+'in'+'d'='FIND'
Can you help me to learn more?
(Other definitions for find that I've seen before include "Discover by chance" , "Come across" , "Track down" , "Realise" , "Acquisition" .)