Pruning honeysuckle

Couple of weekends back our pergola got replaced. Instead of gently rotten and low enough to bang your head, it's now all new and tall(er)and sound :D

Only technical hitch is that it's now about a foot shorter than it was (don't ask!) and at least a third of a huge old honeysuckle is trying very hard to grow out over empty space.

So - what's the best way to handle it? When can I prune it, especially given we're not talking a light haircut here?

 

Now's as good a time as any.

 

'tis done and the pergola is all treated :D Wound up taking off nearly 2/3rds of it. The stems were over 1" across, but did seem to be shooting below the cuts, so fingers crossed.

Thanks for the advice