Faster

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Old English fæst ‘firmly fixed, steadfast’ and fæste ‘firmly’, of Germanic origin; related to Dutch vast and German fest ‘firm, solid’ and fast ‘almost’. In Middle English the adverb developed the senses ‘strongly, vigorously’ (compare with run hard ), and ‘close, immediate’ (just surviving in the archaic fast by ; compare with hard by ), hence ‘closely, immediately’ and ‘quickly’; the idea of rapid movement was then reflected in adjectival use.

wiktionary

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fast(“quick; quickly”) +‎  -er. 

fast(“refrain from eating”) +‎  -er. 

etymonline

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faster (n.)

"one who fasts," c. 1300, agent noun from fast (v.).