(Assume this is a compact or double) It depends how tight you are on large-large plus 1" with your 50t ring. If on the short side then you'll need a chain an extra (one inch) link longer. If on the long side (of 50t-large plus 1"), you'll likely be OK.

One sure-fire way to tell...

You will probably be fine as is.

If you can cross-chain from your current big ring to largest cog, that’s probably similar to using the 53 and not cross-chaining.

If you have the extra links from your current chain you could just add two on, or go two links longer the next time you swap chains.

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ECMGN Therapy Silicon Valley:
Depression, Neurocognitive problems, Dementias (Testing and Evaluation), Trauma and PTSD, Traumatic Brain Injury (TBI)

Hard to say without seeing your setup. Maybe? Most of the bikes I see these days have chains that are too long, so you're probably OK.

You might want a new inner chainring, though. Especially if you've got a 34 on there.

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Tech writer/support on this here site. FIST school instructor and certified bike fitter. Formerly at Diamondback Bikes, LeMond Fitness, FSA, TiCycles, etc.
Coaching and bike fit - http://source-e.net/ Cyclocross blog - https://crosssports.net/ BJJ instruction - https://ballardbjj.com/

Since you will be using 3 more rollers, a pair of links would make your new system nearly the same as it is now.

If you sized your chain to be the longest it could be without sagging in the small/small combo then you'll probably be OK with what you have.

Is there a "rule", like (big ring - little ring ) must be greater than X ?

It depends. Modern chainrings all have ramps/pins that are "clocked" to interface with the other chainring(s) in the set. The allowable variance, well, varies from manufacturer to manufacturer. Also with how much you can deal with, personally, in terms of things not working perfectly.

A 34/53 is pretty much never going to be ideal, but on some bikes and with some riders it'll be OK. Chainstay length will have a fair bit to do with it, also whether it's a disc brake bike or not. With the wider spacing of disc brake bikes, short(er) chainstays make the margin for error with things like this much tighter... this is why a gravel groupset like GRX pushes the crank outboard a bit.

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Tech writer/support on this here site. FIST school instructor and certified bike fitter. Formerly at Diamondback Bikes, LeMond Fitness, FSA, TiCycles, etc.
Coaching and bike fit - http://source-e.net/ Cyclocross blog - https://crosssports.net/ BJJ instruction - https://ballardbjj.com/

When was last time you put a new chain on it? If’s it been a while (more than a year) put a new chain on. If it’s a recently new chain refer to what others said above. New chains are cheap compared to replacing a worn cassette and since you are putting a new chain ring on, treat it to a new chain.

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Mike Plumb, TriPower MultiSports
Professional Running, Cycling and Multisport Coaching, F.I.S.T. Certified
http://www.tripower.org

For sure this. At minimum, always check the chain elongation before swapping rings. If it's more than slightly elongated, you'll put a big dent in both the life of the ring and the life of the chain if you don't swap the chain.

But be really cautious with purchasing new chains these days. There are an incredible number of counterfeits floating around, and it isn't easy to tell the difference if you don't know what you're doing. Until they fail to work correctly, or fail under load.
*Definitely* do not buy something like a Shimano, SRAM, or Wipperman chain on Amazon or Ebay unless you know it's coming from a reputable source.

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Tech writer/support on this here site. FIST school instructor and certified bike fitter. Formerly at Diamondback Bikes, LeMond Fitness, FSA, TiCycles, etc.
Coaching and bike fit - http://source-e.net/ Cyclocross blog - https://crosssports.net/ BJJ instruction - https://ballardbjj.com/