To smear or stain someone or something with grease, oil, or another sticky substance (literal).
2.
Spaininformalcolloquial
To cause someone to suffer inconvenience, trouble, blame, or loss; to set someone up or leave them to deal with the negative consequences (figurative).
Examples:
ES: ¡Y estamos a punto de pringarla!
EN: But three are dead!
ES: No tengas tanta prisa por pringarla. Puedes retirarte.
EN: Don't you be in such a hurry to get yourself starched.