Call for attention having advanced on border (4)
I believe the answer is:
ahem
'call for attention' is the definition.
(I've seen this in another clue)
'advanced on border' is the wordplay.
'advanced' becomes 'a' (abbreviation).
'on' says to put letters next to each other (in a down clue, letters appear on others).
'border' becomes 'hem' (I've seen this in another clue).
'a'+'hem'='AHEM'
'having' is the link.
(Other definitions for ahem that I've seen before include "Noise made when clearing throat (4" , "I say!" , "Attention-getter" , "It attracts attention" , "Expression of disapproval" .)