Installing from a full installer will update the recovery partition.
If that is too much for you, this method works, even though it is old. Originally for El Capitan or older, it works up through Mojave.
See the text below.
Updating your recovery partition. Updating through the mac app store or with the delta or combo update will NOT update the recovery partition.
To make the 10.11.5 recovery partition or later (tested using Mojave, and it worked OK):
1. Download the Lion Recovery Update from
https://support.apple.com/kb/dl1464?locale=en_US . Make sure it is in your downloads folder.
2. Download the full installer for El Capitan 10.11.5–macOS Sierra 10.12.1 etc., from the mac app store, right click on it and click Show Package Contents. Go to Contents/SharedSupport/. Copy the InstallESD.dmg file into your Downloads folder.
3. Download and decompress the file recovery.sh.zip from
http://4unitmaths.com/recovery.sh.zip and move recovery.sh into your Downloads folder if it's not there already.
4. Open Terminal and type the following commands:
chmod +x ~/Downloads/recovery.sh
sudo ~/Downloads/recovery.sh
Wait a few minutes for it to finish and return back to a prompt. Reboot with holding down the option key to test your new recovery partition.
(If you have core storage you will have to revert it to make the recovery partition show up in the startup manager. Just run these in terminal to revert it if you want to:
diskutil cs list
and then
diskutil coreStorage revert lvUUID
where lvUUID is the last lvUUID reported by the previous Terminal command. Then restart.)
Such as
diskutil coreStorage revert Disk1