Jack gives thanks to a redhead (3)
I believe the answer is:
tar
'jack' is the definition.
(both are informal terms for sailor)
'thanks to a redhead' is the wordplay.
'thanks' becomes 'ta' (UK informal version of 'thank you').
'to a redhead' becomes 'r' (head letter of 'red').
'ta'+'r'='TAR'
'gives' acts as a link.
(Other definitions for tar that I've seen before include "Dark viscous stuff" , "prepare for feathers?" , "Seaman; pitch" , "one may need to pay on deck" , "Sailor (colloq.)" .)