Put up at home, having no friend around (8)
I believe the answer is:
nominate
'put up' is the definition.
('nominate' can be a synonym of 'put up')
'home having no friend around' is the wordplay.
'home' becomes 'in' ('he's home' can mean 'he's in').
'having no' becomes 'no' (I've seen this in other clues).
'friend' becomes 'mate' (mate is a kind of friend**).
'around' is an insertion indicator.
'no'+'mate'='nomate'
'in' going inside 'nomate' is 'NOMINATE'.
'at' acts as a link.
(Other definitions for nominate that I've seen before include "Propose as a candidate" , "Pick as a candidate" , "Specify (person for job)" , "Propose - a mention (anag)" , "Propose for office" .)