Trim new shoots back to one of two sets of leaves whenever the tree is growing unless you wish to thicken branches. Trident maples benefit from leaf cutting (defoliation) in summer. I have done this as late as mid July with good results. I have been told that some people practice this defoliation several times in one season on very healthy Trident Maples.
We like to give them a hard prune back in midsummer and again in midwinter. A hard prune back in midsummer encourages the tree to put out lots of small new shoots, these new shoots have time to harden off before the winter. We then thin out the growth in winter. I have found that this thinning out is important, as they tree can’t cope with the profusion on small new shoots, and they can die off, leaving a new shoots.
A number of growers, most noticeably, the late Peter Adams, suggest partial defoliation. He covers this well in his Book, Bonsai With Japanese Maples. Essentially, the process involves the removals of large leaves on the maple all through the growing season. This is a more gentle approach and also gives excellent results.
So, a number of pruning methods. I think the most import message here is to keep them well pruned. When well pruned, they will put out lots of small new shoots and become lovely and dense. Once this happens, remember to thin this new growth to prevent die-back.