The only relevant standard error is that of the log of the hazard ratio. You will note that the 95% confidence interval is not symmetrical about the hazard ratio estimate. You can't calculate a standard error from that.

Meta-analyses of all ratio measures (e.g., risk ratio, odds ratio, response ratio) are run on the log of that measure. The standard error is thus calculated on the log value of that measure, The 95% CI of the log value is then calculated and then back-transformed to a non-log 95% CI.

In some meta-analysis , the seln(HR)=[ln(ul)-ln(ll)]/(1.96*2) would be usesd.

Gordon L Warren Thanks for the insights, we will go with the study with symmetric confidence intervals. Sen Wang Thanks for the answer.

SE of logHR=sqrt(4/E) where E is the total event size; or sqrt(1/E1+1/E2) where E1 and E2 are the events for two arms respectively