The Hip Strap (shown in red on the diagram) supports the breeching. 

These are replacement straps, designed to suit the Classic Complete Breeching (available in Small Pony, Pony, Cob, Full Size, and Extra Full Size)

Length: 105cm (41") 
Width: 19mm (3/4") 
Pony Size

Length: 113cm (44") 
Width: 19mm (3/4") 
Cob Size 

Length: 118cm (46") 
Width: 19mm (3/4") 
Full Size