Hi Sreekesh,
Thank you for being patience.
Our further analysis, Currently our code library does not support to hiding the tabpages in TabBarSplitter control, but we can achieve this to remove and add it again the tabpage in TabBarSplitter control.
Please refer the following simple sample and let me know if this helps to you.
http://websamples.syncfusion.com/samples/Tools.Windows/F75415/main.htmPlease let me know if any concerns.
Regards,
Hema