After getting access to the key and connecting as a client to your router, the attacker can potentially launch a MITM (Man In The Middle) attack at your router using a technique called as ARP spoofing.
https://en.wikipedia.org/wiki/ARP_spoofing
Consequently, if successful, he can get access to the traffic of other clients on the network. He can intercept and eavesdrop on traffic and in some cases such as cleartext HTTP, he can modify the and inject malicious data.
Moreover, if the MITM attack is successful, the attacker can possibly intercept the credentials to access the router such as in the case of TP-Link WR740N router which has an authentication system wherein the credentials are sent in cleartext(base64 encoded) and can be trivially decoded. He can use these credentials to gain access to the router at which point, he can launch other attacks.
Hope that helped.