S. R. Faruqi:

dast = claw
yaum ul-.hisaab = Doomsday [qiyaamat kaa din]

It's said that on Doomsday [qiyaamat], the oppressed will seize the garment-hem of their oppressors and demand justice. He has presented the scene of spring, that as the garment-hem of flowers sprang up (that is, where flowers were numerous), Nightingales too kept on becoming numerous. But the flight of imagination has carried away this thought in such a way that the hand of the Nightingale and the garment-hem of the rose were springing up together-- as the garment-hem of the rose spread, along with it the hand of the Nightingale too grew up, and became entangled with the flower as if the Nightingales would be demanding justice.

On the basis of this kind of entanglement of the hand of the Nightingale and the garment-hem of the rose, it seemed that Doomsday had broken out in the courtyard. For the 'hand of the Nightingale' to 'spring up' is a fine effect. The courtyard of the garden is a place, and Doomsday is a time. To use a place [makaan] as a simile for a time [zamaan] is also a superb thing.

Al-e Ahmad Surur told me that in the opinion of Asar Lakhnavi, the 'hand of the Nightingale' referred to the outer green leaves of the bud, which are called in English 'calyx'. When the bud blooms, then those leaves separate and take on the shape of a claw. And the petal part of the flower, which in English is called 'corolla', is as if in the grip of this 'claw'. This interpretation is very interesting, and the probability is that it might also be correct.

But for the calyx, 'hand of the Nightingale' is neither a metaphor nor an idiom. We can certainly call it an 'allegory' [tam;siil]. And the success of an allegory occurs when its dictionary meaning too is manifest. In Asar Lakhnavi's interpretation the dicionary meaning is not manifest, because for calyx, the metaphor 'hand of the bird' might perhaps work, but there's no legitimation [javaaz] for 'hand of the Nightingale'. In any case, Asar Sahib's interpretation does call attention to the words of the verse.

FWP:

SETS == WORDPLAY
MOTIFS == DOOMSDAY
NAMES == NIGHTINGALE
TERMS == ALLEGORY; WORDPLAY

SRF here supplies for tam;siil the English word 'allegory', and gives some sense of the use of the term as well.

Asar Lakhnavi's idea is not very compelling. Falling at the beloved's feet and desparately grasping (or seeking in vain to grasp) her garment-hem is such a classic ghazal thing for the lover to do-- and grasping at the trailing garment-hem of a long-skirted robe is not at all like imprisoning rose-petals in a 'claw'. See the definition above for 'seizing the garment-hem' [daaman paka;Rnaa], with its many relevant senses, including pleading, surrendering, seeking protection, and accusing-- thus the relevance of invoking the 'Day of Accounting', or Judgment Day.

Hovering over the verse, as SRF notes, is the identification of the day of reckoning or 'Day of Accounting' with the far more commonly used qiyaamat , the 'Doomsday' when the dead will rise up; the source of that word is qiyaam , meaning 'standing upright; rising up; up-rising, insurrection' (Platts p.796). The appropriateness of this sense to the springing up of flowers is obvious. Moreover, the secondary effects of Doomsday, such as 'commotion, uproar, excess, extraordinariness, wonderfulness, grievousness' (see the definition above) are also enjoyably descriptive both of the cosmic turbulence of spring, and of the oppressed and suffering Nightingales' clamor for justice. And if we consider the general idiomatic use of qiyaamat in Urdu as 'a wild scene, an extreme turmoil', then all sorts of passionate 'seizing of the garment-hem' could be going on in the courtyard, including ones that have nothing directly to do with a literal Judgment Day. For more on such hovering, unstated cases of wordplay, see {20,1}.