Hereditary Peerages (Succession) Bill currently before the House of Lords seems to reinforce discrimination by requiring that not only is the woman to be oldest surviving

child legitimately born to the incumbent bur that that additional hurdles must be met:

Section 2 Requirements for succession by female heirs

The requirements of this section are that—
(a) the incumbent of an hereditary peerage (“the incumbent”) has, in accordance with the requirements of section 3, petitioned the Lord Chancellor in writing for a certificate establishing future succession;
(b) a certificate has been issued in accordance with section 4; and(c) any female heir succeeding to that hereditary peerage— (i) has attained the age of 21 years;

Section 4 says “Any legitimate child of the incumbent of that peerage may lodge an objection
(“an objection”) in response to that petition within 3 months of its publication.”
Section 4(4) goes on to say the Lord Chancellor may invite the persons who submits …the petition and objection or objections to (consider):
(i) the financial consequences of so doing for the child making the
objection; and
(ii) whether or not the succession had been promised to the child making the objection.
No matter what your belief about peerages, is such discrimination against women just In this age, why not the full rights as applied to males, without clarification?  Who and what next?
(Hereditary Peerages (Succession) Act 2012).