I have observed upregulation of p21 with G0/G1 cell cycle arrest in case of my drug treatment. How I can explain this result? Shall I do any further study to understand the mechanism properly?
p21 is a cdk inhibitor which action is to stop cell cycle at G1/S transition. It can be induced in a p53-dependent manner so if your drug treatment activates p53 you get more p21.
As noted by Dominique, being a CDK inhibitor, it is likely that increased levels of the p21 in your system following a drug treatment contribute to a cell cycle arrest. Notably, the levels of p21 could be regulated in p53-dependent and independent manner. Additionally, other CDKs also contribute to cell cycle arrest. Therefore, if needed, I would check whether the p53 is functional or not, it is activated or not, and whether other CDKs are also regulated by the drug.