Initially embarrassing mistake to pass (6)
I believe the answer is:
elapse
'pass' is the definition.
(I've seen this before)
'initially embarrassing mistake' is the wordplay.
'initially' indicates taking the first letters.
'mistake' becomes 'lapse' (lapse is a kind of mistake**).
The initial letter of 'embarrassing' is 'e'.
'e'+'lapse'='ELAPSE'
'to' is the link.
(Other definitions for elapse that I've seen before include "Go by - pass away" , "Glide by" , "pass in silence" , "Go past" , "(Of time) go by" .)