As originally enacted, this Act was named:
An Act to shorten the Time now required for giving Notice of the Royal Intention of his Majesty, his Heirs and Successors, that the Parliament shall meet and be holden for the Dispatch of Business, and more effectually to provide for the Meeting of Parliament in the case of a Demise of the Crown.
and the relevant provision was:
That whenever his Majesty, his Heirs or Successors, shall be pleased, by and with the Advice of the Privy Council of his Majesty, his Heirs or Successors, to issue his or their Royal Proclamation, giving Notice of his or their Royal Intention that Parliament shall meet and be holden for the Dispatch of Business on any Day being not less than fourteen Days from the Date of such Proclamation, the same shall be a full and sufficient Notice to all Persons whatever of such the Royal Intention of his Majesty, his Heirs and Successors, and the Parliament shall thereby stand prorogued to the Day and Place therein declared, notwithstanding any previous Prorogation of the Parliament to any longer Day, and notwithstanding any former Law, Usage, or Practice to the contrary.
The Act is about "prorogation", which is a formal end to the Parliamentary session. Between general elections, there can be several sessions, each beginning with a King's Speech announcing the planned business.
It was within the power of the Crown to declare a prorogation to a named date. Parliament could not meet, and therefore could not pass laws and so on, until that date came around. The 1797 Act is saying that during that interval, the Crown can decide that Parliament can come back early. The new date must be fourteen or more days in the future, but can be before the originally named date.
Before this Act, there was a limited power to shorten the prorogation in case of certain emergencies. The Militia Act 1786 was an example (consolidating several earlier statutes), saying that in cases of "actual Invasion or upon imminent Danger thereof, and in all Cases of Rebellion or Insurrection", the King could call out the militia and also summon Parliament back if they were adjourned or prorogued. There does not seem to have been a general prerogative power to shorten a prorogation. See Blackstone's "Commentaries on the Laws of England" (1800 ed.), vol. 1, footnote on p. 187.
The Act therefore does give a new general power, because it is not limited to extreme emergencies. But it also does restrict royal authority, because the formula "by and with the Advice" means that the King is not the decision-maker: it's an action controlled by the government of the day.