Tim initially tiny and cute (4)
I believe the answer is:
twee
'cute' is the definition.
(I've seen this before)
'tim initially tiny' is the wordplay.
'initially' indicates taking the first letters.
'tiny' becomes 'wee' (I've seen this before).
The initial letter of 'tim' is 't'.
't'+'wee'='TWEE'
'and' is the link.
(Other definitions for twee that I've seen before include "Niminy-piminy" , "Sickly sweet" , "Mawkish" , "Small and pretty" , "Overly sentimental or pretty" .)