Clue: Support city welcoming Republican movement a swimmer might start? (10)
Answer: BACKSTROKE
Explanation: Definition: movement a swimmer might start
 BACK(to support/to champion) + STOKE(short for Stoke-on-Trent, city in Staffordshire, England) **containing**(welcoming) R(abbrev. for "Republican", a member of the Republican Party).
Start of a backstroke event: