Just beginning to seem intimate (6)
I believe the answer is:
simply
'just' is the definition.
('simply' can be a synonym of 'just')
'beginning to seem intimate' is the wordplay.
'beginning to' suggests taking the first letters.
'intimate' becomes 'imply' (I've seen this before).
The first letter of 'seem' is 's'.
's'+'imply'='SIMPLY'
(Other definitions for simply that I've seen before include "Merely, just" , "Without fuss" , "In a straightforward manner" .)