Strange desire to live (6)
I believe the answer is:
reside
'live' is the definition.
(synonyms)
'strange desire' is the wordplay.
'strange' is an anagram indicator.
'desire' is an anagram of 'RESIDE'.
'to' acts as a link.
(Other definitions for reside that I've seen before include "'Live, dwell (6)'" , "Make one's home permanently" , "Dwell permanently" , "Inhabit" , "Live in permanently" .)