The most common and most likely answer to this crossword clue is the 8 letter word SKEETERS
I've seen this crossword clue in The Guardian
S
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Buddy explains!
The straight part
We know that "Trump’s ‘pesky bugs’" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case trump’s ‘pesky bugs’ = skeeters.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does SKEETERS mean?
SKEETERS noun- Mosquito
- To move hurriedly or as by bouncing or twitching; to scamper, to scurry.
- To make a scratching or scuttling noise while, or as if, skittering.
- To move or pass (something) over a surface quickly so that it touches only at intervals; to skip, to skite.
- To cause to have diarrhea.
- To suffer from a bout of diarrhea; to produce thin excrement.