The top of carpet pile must be tacky (5)
I believe the answer is:
Here is my best explanation:
'tacky' is the definition.
('cheap' can be a synonym of 'tacky')
'the top of carpet pile' is the subsidiary indication.
'the top of' says to take the initial letters.
'pile' becomes 'heap' ('heap' can be a synonym of 'pile'**).
The first letter of 'carpet' is 'c'.
'must be' is the link.
(Other definitions for cheap that I've seen before include "low in price", "Of very poor quality", "Inexpensive or tastelessy showy", "Budget -cheesy", "good value", "Vulgar", "Shoddy", "Low in price or tastelessly showy", "Contemptible" and "Mean".)