You can run BLAST for primer pairs as in the corresponding tool. This tool allows one to screen primers against user-selected database in order to avoid primer pairs that can cause non-specific amplifications. You primers should have Primer3 UGENE format. Either get them using Primer3/Primer3 (no target sequence) or create by using the special Transform into a primer pair feature.

Select primer pairs you need to BLAST:

Click right mouse button → Analyze → Query NCBI BLAST database...:

The foolowing dialog has absolutely the same settings as the regular Remote BLAST tool, except:

• Instead of "Save annotation(s) to" and "Annotations paramters" settings you can see a list of selected primer pairs. That means, that BLAST will be run three times for three primer pairs - pair 1, pair 4 and pair 3. All results will be stored to the annotation group with a primer pair, which was an input for this calculation.
• The "Megablast" option is enabled by default. Disable this option to get more results (it affects calculation time).