An air base regularly getting bills (4)
I believe the answer is:
nibs
'bills' is the definition.
('nib' can be a synonym of 'bill')
'an air base regularly' is the wordplay.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'an'+'air'+'base'='anairbase'
The alternating letters of 'anairbase' are 'NIBS'.
'getting' acts as a link.
(Other definitions for nibs that I've seen before include "VIPs?" , "Writing tips of old pens" , "Writing points" , "Pen points" , "Points of pens" .)