Thats simple, set wlan1 of RB433 to Station mode or better Station Bridge, wlan2 to AP Bridge mode and set also SSIDs (wlan1 SSID must match with the Linksys AP connected and wlan2 SSID you can choose whatever you want your network to be named). Note that in 2,4GHz only 3 channels from available 13 (or 11 in US) doesnt overlap so choose one as far as you can from the one used by Linksys AP.
Regarding the IP addressing it depends if you want to do a bridge and use same IP address range like the Linksys, or if you will use routing. Bridging is maybe more simple so create a bridge and add wlan1 and wlan2 to the bridge (Winbox → Bridge → Ports) and if wlan1 connects to the Linksys AP you should be able to browse internet when connected to the wlan2, you should get the IP adress assigned by LInksys DHCP (if its configured)
BTW : Linksys AP isn’t the DHCP server for the network. It acts as a bridge with no viewable IP address. The IP addresses are assigned by the main router, and there is no way to tell what’s the AP IP address is.
You have two wireless interfaces on your RB, so no need to do a repeater. In case Linksys is in the bridge mode and you have no access to it, then you cant use WDS and creating a bridge on the RB as it will most probably not work. I would do it this way:
Set wlan1 of your RB to station mode and connect it to the Linksys AP, use DHCP on this interface or assign a static IP from the range the main router provides to clients via DHCP. You also need to set default gateway and configure masquerade (NAT) for packets going out of wlan1.
Then configure wlan2 as AP bridge, assign whatever IP address you want (outside the IP range used on the Linksys of course), configure DHCP server and you are done.
Do not add both wlan interfaces to Bridge if you want routing which apparently you want. You should add only ether1 (or also ether2 and 3) and wlan1, wlan2 is in another network (Linksys) so not a member of bridge.
/interface bridge port
add bridge=Bridge interface=wlan1
add bridge=Bridge interface=wlan2
All your interfaces are disabled? No No No
set time disabled=yes display-time=5s
set resources disabled=yes display-time=5s
set uptime disabled=yes display-time=5s
set packets disabled=yes display-time=5s
set bits disabled=yes display-time=5s
set version disabled=yes display-time=5s
set identity disabled=yes display-time=5s
set Bridge disabled=yes display-time=5s
set wlan1 disabled=yes display-time=5s
set wlan2 disabled=yes display-time=5s
set ether1 disabled=yes display-time=5s
set ether2 disabled=yes display-time=5s
set ether3 disabled=yes display-time=5s
If I understand correctly the Linksys network is not secured?
Try this config but before doing this make:
/system reset-configuration no-defaults=yes
then configure some static IP on your PC and connect to the Mikrotik via MAC address from winbox and paste this: