A medical word, tardive is an adjective meaning that a symptom is slow in appearing, or appears late in a disease. It may be a side effect that appears only after you have been taking a drug for a long period (i.g. tardive dyskinesia), a symptom that appears after you have had the disease for a long time (i.g. tardive cyanosis), or simply something (usually something bad) that appears late in the course of human development. I have also found one example of tardive being used in physics, to describe an effect in which "thermal power... develops long after the termination of electric input power"*
Tardive is nothing more or less than the feminine form of the French word tardif, meaning late or tardy. Old French tardif is also the root word of 'tardy' and 'retard'. Tardive apparently didn't enter the English language until the 1960s (probably in 1964, originally only as part of the phrase tardive dyskinesia), which no doubt accounts for its comparative obscurity.
If you are a wine buff, you may also come across the French term vendange tardive, meaning a late harvest. Grapes harvested late in the year are sweeter, and the resulting wines may have a sweeter palate, and have a higher alcohol content.