A new kiss promises to be tense (7)
I believe the answer is:
anxious
'be tense' is the definition.
(thesaurus)
'a new kiss promises' is the wordplay.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'kiss' becomes 'x' (X can represent a kiss).
'promises' becomes 'IOUs' (promises to pay a debt).
'a'+'n'+'x'+'ious'='ANXIOUS'
'to' is the link.
(Other definitions for anxious that I've seen before include "Nervy" , "Restless" , "Uneasy, worried" , "Apprehensive, uneasy" , "Jittery" .)