Outlaw captured by a fellow in desert (7)
I believe the answer is:
abandon
'desert' is the definition.
('abandon' can be a synonym of 'desert')
'outlaw captured by a fellow' is the wordplay.
'outlaw' becomes 'ban' (banning is a kind of outlawing).
'captured by' means one lot of letters goes inside another.
'fellow' becomes 'don' (I've seen this before).
'a'+'don'='adon'
'ban' inserted inside 'adon' is 'ABANDON'.
'in' acts as a link.
(Other definitions for abandon that I've seen before include "Desert or yield without restraint" , "ditch" , "Walk out on" , "Forsake, leave behind" , "Forsake with recklessness" .)