According to several websites used for help with crossword puzzles, the most likely 4-letter answer to the clue "glance furtively" is "peek". Peek is a verb that means "to glance quickly" or "to look or peer furtively". Another word that also might work is "leer", which can be defined as a "furtive glance". Though a bit less likely than both of these, the words "peer" or "peep" could also be correct.
The word "furtively" means "in a furtive manner", while "furtive" means "characterized by stealth; surreptitious". So to glance furtively specifically refers to glancing in a secretive manner. For this reason, the word "look" is a possible but unlikely answer.
Some other synonyms of peek which aren't possible answers to this clue are: glance, glimpse, spy, and glint. So while it's most likely that "peek" is the answer to this clue, check with the specific puzzle to make sure it fits with the other letters and words you have already entered.