You haven't provided specifics as to your box - are you using uEFI, Secure uEFI or BIOS in booting? I'll assume BIOS and walk through a common process I do.
For my own boxes (where I QA-test and install releases many times per week) and often have 1-6 (GNU/Linux but mostly Ubuntu flavors) systems installed on a box, the last installed will always end up owning the grub and after validating all is good with the last QA-test install (& reporting the test on iso.qa.ubu.com...),
I boot the system I want to own grub and
sudo update-grub
sudo grub-install /dev/sda
I use the first update-grub
command so it's made aware of my last install and any changes (say a Lubuntu hirsute daily which may have a later kernel than the prior install present). Secondly I make that OS take ownership of the MBR (master boot record) of the disk the BIOS system boots (in this example it's my Debian Bullseye/sid; I don't test on my primary system which runs Lubuntu).
I've assumed BIOS for this, following steps I do very regularly on one box in particular but adjust for your specific box; on some it won't be /dev/sda