Determined person not getting on is needing shelter (10)
I believe the answer is:
persistent
'determined' is the definition.
(I've seen this before)
'person not getting on is needing shelter' is the wordplay.
'not getting' is a deletion indicator.
'needing' says to put letters next to each other.
'shelter' becomes 'tent' (tent is a kind of shelter).
'person' with 'on' removed is 'pers'.
'pers'+'is'+'tent'='PERSISTENT'
(Other definitions for persistent that I've seen before include "hanging on" , "Prolonged; nagging" , "Determined" , "Dogged" , "fixed" .)