If the hijri year has passed on wealth that meets the nisaab (threshold for zakaah), it is obligatory to pay zakaah immediately; it is not permissible to delay it after it has become due if one is able to pay it.
Allaah says (interpretation of the meaning):
“And march forth [lit. hasten] in the way (which leads to) forgiveness from your Lord, and for Paradise as wide as the heavens and the earth, prepared for Al-Muttaqoon (the pious)”
[Aal ‘Imraan 3:133]
“Race with one another in hastening towards forgiveness from your Lord (Allaah), and Paradise the width whereof is as the width of the heaven and the earth, prepared for those who believe in Allaah and His Messengers”
Moreover, if a person delays that, he does not know what will happen to him. He may die leaving this obligation unfulfilled; fulfilling one's duty is obligatory.
Also the poor may be depending upon that, and if he delays it, the poor will remain needy and not have enough to meet their needs. See al-Sharh al-Mumti’, 6/197
The Standing Committee was asked about a man who possesses the nisaab in Rajab but wants to delay paying zakaah until Ramadaan. The committee replied:
It is obligatory for you to pay zakaah in Rajab in the year following the year in which you took possession of the nisaab. But if you want to pay it in Ramadaan of the year in which you took possession of the nisaab, paying it before the year has passed, that is permissible, if there is a valid need for it to be brought forward. But delaying it until the Ramadaan that comes after the year has passed and it has become due in Rajab is not permissible, because it is obligatory to pay it as soon as it becomes due.
Fataawa al-Lajnah, 9/392.
Whoever is obliged to pay zakaah and delays it with no valid shar’i excuse is sinning, because the evidence of the Qur’aan and Sunnah shows that zakaah must be paid as soon as it falls due.
According to another fatwa (9/398):
It is not permissible to delay paying zakaah after the year has passed, unless that is for a valid shar’i excuse, such as there being no poor people at the time when the year has passed, or not being able to get the zakaah to them, or because the money is not available, etc. But delaying it until Ramadaan is not permissible unless the period is very short, such as if the year will have passed in the second half of Sha’baan, in which case there is nothing wrong with delaying it until Ramadaan.