Started new pill qlaira (not on first day of period)missed 2 periods, negative blood and urine pregnancy tests. Never skip pill. Causes?

Likely normal. Some people get no periods on the pill even when taking the pill correctly. This is because the hormones in the pill are so balanced in that person that no lining of the uterus grows so there is nothing to shed as a period. This is not a problem.
See below. This could be the new pill or a thyroid condition or other conditions such as pcos.