促 means “urge, prompt”

うながす · unagasu

Also: stimulate, press, demand

Kun'yomi (Japanese reading)
うながす
On'yomi (Chinese reading)
ソク

JLPT N1 · Taught in secondary school · 9 strokes

The story

A person (亻) with a foot (足) planted right behind them: picture someone nudging you along. 促す is to prompt or urge, 催促 is pressing for a late payment or reply, and 販促, short for 販売促進, is sales promotion.

Used in 促す (unagasu, to urge/prompt), 催促 (saisoku, pressing/reminder), and 促進 (sokushin, promotion/acceleration)

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Readings from KANJIDIC2, © EDRDG, CC BY-SA.