John Gill Commentary Psalms 66:13

"I will come into thy house with burnt-offerings; I will pay thee my vows," — Psalms 66:13 (ASV)

I will go into your house with burnt offerings
The psalmist here represents the saints and faithful in those times, who being delivered out of all their troubles, and brought into a large, free, plentiful, and comfortable condition, will come together into the place of public worship, and there unite in their sacrifices of praise to God; will come and present themselves as a whole burnt offering to the Lord; will come with hearts inflamed with love to God and one another, which is more than all whole burnt offerings and sacrifices, (Mark 12:33) ;

I will pay you my vows ;
thanksgivings promised in time of distress, as follows; see (Psalms 50:14) .