Thank you for your question about pruning your elm tree.  The optimum time to prune elm trees is late fall through early spring, and the window of time is still open, but closing.  If your elm is a species that is susceptible to Dutch Elm Disease the  elm bark beetles that spread this fungal disease emerge in late spring.

Pruning before the tree leafs out allows you a better view of branches so that you can determine which need to be removed.  Make sure that pruning equipment is sterilized before use to prevent disease and that proper cuts are made to ensure prompt healing of the wounds.

Here is a publication by Washington State University on the pruning of elms:

https://ppo.puyallup.wsu.edu/elm/22-2/

Here's a publication from Purdue on making proper pruning cuts.

https://extension.purdue.edu/extmedia/FNR/FNR-506-W.pdf

Good luck with your spring pruning.