Support for climbing plants (7)
(Other definitions for pergola that I've seen before include "Bower" , "Arch for garden plants" , "Trellis-covered walk" , "Garden frame for climbers" , "Arched frame for climbing plants" .)
'support for climbing plants' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for trellis that I've seen before include "supporting frame" , "Support for creepers" , "climbers train on it" , "Lattice structure" , "Latticework for climbing plants" .)