Two relevant parts here:
41.5 Any Players registered with a Club after 5.00pm on the fourth Thursday in March in each Season will not be eligible to play in any match organised by The League, except as permitted in Regulation 54.
AND
54 Emergency Loan of Goalkeepers
54.1 If all the professional goalkeepers at a Club are either certified by an independent medical practitioner as being unfit to play or are suspended, a Club may register (either before or after the deadlines laid down in Regulation 53.3.4), a further goalkeeper on a short term Emergency Loan in accordance with the following provisions:
54.1.1 the Executive shall allow a Club to sign such a goalkeeper for a period of 7 days (notwithstanding the provisions of Regulation 53.3.9), inclusive of the starting date and finishing date;
54.1.2 any such short term Emergency Loan shall be subject to The League, in appropriate circumstances, having received (including by facsimile) the appropriate medical certificate(s) together with the appropriate form(s) for his registration not later than 3 hours prior to kick off and the Executive having confirmed that the circumstances conform to the provisions of this Regulation;
54.1.3 the period of any short term Emergency Loan of a goalkeeper may be renewed for 7 days at a time but further medical certification must be provided on each occasion;
54.1.4 any short term Emergency Loan in respect of the same goalkeeper may not exceed 93 days during any Season; and
54.1.5 the provisions of Regulation 52.2.2 shall not apply to the Emergency Loan of a goalkeeper.