Historically, any military operation in which Saudi Arabia has committed itself quickly includes Pakistan. A long-standing ally in the Sunni world, Pakistan is usually a given, and Saudi Arabia is unsurprisingly courting them for the Yemen war.
Pakistan’s Defense Ministry is confirming that they are taking the request seriously, but it’s not nearly the slam dunk it had once been, as the consequences of involvement could be grave for Pakistan.
Yes, Pakistan’s military is already overstretched both with omnipresent tensions along the India border and the ongoing wars against Islamist factions within their own tribal areas. Committing anything more than a token offering would be difficult for Pakistan because of that.
It is also a huge risk because of Pakistan’s significant Shi’ite minority. The Saudi war in Yemen is by design an aggressive war against Shi’ite power in neighboring Yemen, and trying to undermine that through force of arms will doubtless rile Shi’ites across the region. To the extent Pakistan is involved with the war, the unrest among their own Shi’ites will be all the greater.
Pakistan’s aspirations of being a regional player within the Muslim world certainly are helping to push them into involvement, but the dangers associated are tempering that interventionist zeal in this case, and might force them to wait for a more opportune intervention.