Wireless router compatability

Yes, it will work, as long as your make sure your new router is configured to support the 802.11 standard your Macbook Pro supports.

• 802.11b (old and slow; 11megabits/sec) is supported by every WiFi devices and router
• 802.11g (still commonly used; 54megabits/sec) is commonly used in many devices, especially a lot of handheld devices, and you Macbook Pro supports it.
• 802.11n (the previous greatest thing since sliced bread; 300megabits/sec "In Your Dreams") has been around for awhile, and is in most Macbook Pros for the past many years, so chances are yours supports it as well
• 802.11ac (the new kid on the block; gigabit/sec "pull the other finger") is the current standard rolling out. Not many devices support 802.11ac yet, and I do not think they have any low power chips that would work well in handheld devices yet.

There was an older 802.11a standard that is mostly not used, but a lot of equipment supports it because it was a standard.

And then there is 2.4GHz radios and 5GHz radios. Chances are your Mac has support for both 2.4GHz and 5GHz radios.

And WPA2 encryption standards. Again, chances are your Macbook Pro also supports WPA2 (it has been around for years).

Any new router is going to support ALL of these WiFi protocols, and new routers that cost more than a few dollars are going to have 2 radios to support 2.4GHz and 5GHz.

Now it is always possible for a WiFi router to be configured so it turns off a given radio frequency, or is told to not speak a given protocol, but that would be something you did as part of the setup. The default would be to support everything.