Lofty is beginning to tower over everyone (4)
I believe the answer is:
tall
'lofty' is the definition.
(synonyms)
'beginning to tower over everyone' is the wordplay.
'beginning to' suggests taking the first letters.
'over' means one lot of letters go next to another (in a down clue, some letters go over others).
'everyone' becomes 'all' (all people).
The first letter of 'tower' is 't'.
't'+'all'='TALL'
'is' is the link.
(Other definitions for tall that I've seen before include "hard to believe in" , "Unbelievable" , "that's hard to swallow" , "Lofty; unlikely" , "Higher than the average person" .)