I'm a 36 year old woman pregnant with my first child. My first pregnancy ended in miscarriage - trisomy 23. Should I get a cvs test?

Talk with your OB. The risk for trisomy increases for women over age 35. A number of different chromosomal abnormalities - including different trisomies - can happen at any age. Most often, these cause severe problems and the pregnancy is lost. Rarely a trisomy or other chromosome problem is the result of a rearrangement that one parent silently carries. Be sure show your OB the test results from your miscarriage.
Personal decision. Cvs is helpful if you think you would want end the pregnancy in the first trimester based on the results and for genetic counseling for future pregnancies. If you don't think you would end the pregnancy, you may want to consider waiting until your second trimester to get an amniocentesis, it is lower risk and will still give you the genetic information you are looking for.
Other methods too. You can have non-invasive testing (NIPS) done as early as 8 weeks. It takes fetal cells found circulating in mothers blood to do testing similar to CVS. (and not as risky)