Is there any way to update my 2010 iMac

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Sorry, no.

Your iMac can only run up to macOS High Sierra. If you need to upgrade to macOS High Sierra, get it here: How to get old versions of macOS - Apple Support. Backup first!

Jack

No, I would strongly recommend replacing a 2010 iMac with a newer Mac. There are many solutions available to you, if you interested here are a few:

• Buy a new M1 based Mac Mini, for less than $1100 you have a new computer that far out performs your 2010 and you can have new display. You can finance these with zero interest for 12 months.
• Buy a new M1 based 24" iMac with 16 GB of RAM and a 1 TB SSD. More expensive than a MM but an awesome solution.
• Can't afford new, buy an Apple refurbished Mac. There is no downside to this solution. These are identical to a new Mac, you can save hundreds of $$$, they have the same warranty as new, are eligible for AppleCare. I've never had a problem buying one.
• Still too expensive, buy a use Mac from a reputable reseller such as Macsales.com.

⬆️ Not possible. See my response above. ⬆️