Hat having pulse, that is (6)
I believe the answer is:
beanie
'hat' is the definition.
(I've seen this before)
'pulse that is' is the wordplay.
'pulse' becomes 'bean' (I've seen this before).
'that is' becomes 'ie' (synonyms).
'bean'+'ie'='BEANIE'
'having' is the link.
(Other definitions for beanie that I've seen before include "Small close-fitting hat" , "cap" , "Topping" , "one on the head" .)