How do I connect my new macbook pro (with only thunderbolt 3 ports) to a 2011 display?
MacBook Pro (13-inch, Late 2016, 4 TBT3), iOS 10.3.1, Display is 2011, Model Number: A131
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The right connector is a MagSafe or MagSafe-2 OUTPUT of the display power supply. At this writing, it can not be used to charge your new MacBook Pro directly. It is not required for anything in the display.
The center connector is a USB A-connector, for USB-1 or 2. It is not required by the display unless you wish to use the display's USB ports. (except a few Mac displays use USB to run their Brightness settings).
The left connecter appears to be either a Mini DisplayPort or ThunderBolt (1 or 2) port.
a) If a [Mini] DisplayPort, you need a third-party adapter to [Full size] DisplayPort, and an additional adapter (just a re-wire) to [Mini] DisplayPort. The Apple adapter from USB-C ThunderBolt to ThunderBolt-2 will explicitly NOT work in this case. Adapters direct from USB-C ThunderBolt to [Mini] DisplayPort are just starting to appear in the marketplace.
b) If ThunderBolt, you likely Do need the Apple USB-C ThunderBolt to ThunderBolt (1 or 2) adapter.
Often the Icon on the connector will tell you its type. If you could post more information about the display, we could look up its specs and tell as well.