This is the 1182nd most frequent Korean word.
여당의
Ruling party's.
Here, "여당의" describes the possession of the policy belonging to the ruling party.
여당의 정책은 경제 회복에 초점을 맞추고 있습니다.
The policy of the ruling party is focused on economic recovery.
"여당의" modifies "새 법안" to denote that the new bill is associated with the ruling party.
많은 시민들은 여당의 새 법안을 지지합니다.
Many citizens support the ruling party's new bill.
In this case, "여당의" defines whose stance is being referred to -- that of the ruling party.