I have 550 Quad with the below Spec.

DAYA 550 folding frame
NAZA m lite Flight Controller with GPS
DYS F30A 30amp 4 in 1 BLHeli_S ESC 2-6S
Sunnysky 2216-1100kv Motors
Turnigy Mobius 2-Axis Gimbal with Tarot Controller and AX2206 Motors with Mobius camera
Eachine TS840 5.8G 40CH 600mw AV FPV Transmitter Module
AGA-Power 10000mah 30c 4s lipo battery
11x5 APC slowfly props

The Quad gave smooth hovering with 3000mah 3s lipo, but the flight duration was max 10 mins. I decided to increase the flight time with the larger capacity lipo I upgraded to AGA-Power 10000mah 4s lipo. This 4s lipo alone weights 830gms, with the lipo the total quad weights comes to 2.25kg.
With this weight can the quad have a smooth hovering and longer flight duration.

Note: I have not done the test flight after upgrading the lipo. 

If the quad was hovering fine with 3S I don't think the same PIDs will work with 4S and a different weight. You might want to use something like 9443 props for a 4S setup.

Do 2216-1100kv Motors are good for this setup?

Bump...

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With increased weight your motors will draw more current but you might get 17-22-/+4 min approx, considering you have same props as before.

Which is the suitable motor for the spec.. 
Thinking of Gartt 3508 700kv motors with 12x3.8 propeller?

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I tried today with 10k mah lipo for the same setup and I my hovering time was 11mins.

Do I need to upgrade my motors to Gartt 3508 700kv motors with 12x3.8 propeller?

It is much lesser than what calculated. there is something wrong with your setup which is reducing efficiency. try reducing prop diameter if you have. if you get 11 min in hover it will further reduce in maneuver.

My fault, my charger was having 3000mah max charging cutoff set, So the battery was not fully charged for 10kmah, Need to try again with fully 10kmah capacity..

Use ecalc....
https://www.ecalc.ch/xcoptercalc.php