This uses charade (joining word parts) combined with deletion - you need to remove specific letters from one of the parts before joining them together.
Take 'win' as your first part. Then find a word meaning 'limper' and remove 'member' (specifically 'MP' for Member of Parliament) from it. Join the results together.
Answer: GAINLIER | GAIN (win) + LIMPER with MP (member of parliament) removed gives LI[MP]ER → LIER. GAIN + LIER = GAINLIER (more graceful)