The specific line that the question refers to the adjustment to the standard deduction due to line 39a on the 1040; this originates in law in 26 USC 63, part of the Internal Revenue Code (1986). Specifically, 26 USC 63 (f)(1):
(1) Additional amounts for the aged The taxpayer shall be entitled to an additional amount of $600—
(A) for himself if he has attained age 65 before the close of his taxable year, and
(B) for the spouse of the taxpayer if the spouse has attained age 65 before the close of the taxable year and an additional exemption is allowable to the taxpayer for such spouse under section 151(b)
As a part of the standard deduction, it was not repealed by section 11041 (which repeals the personal exemption, or more specifically sets it to $0). Section 11011, which increases the standard deduction, does not wipe out the currently existing code; rather, it replaces only the dollar amounts - by replacing the previous dollar amount:
(A) INCREASE IN STANDARD DEDUCTION.—Paragraph (2) shall be applied—
(i) by substituting ‘$18,000’ for ‘$4,400’ in subparagraph (B), and
(ii) by substituting ‘$12,000’ for ‘$3,000’ in subparagraph (C).
Of course those amounts are not the 2017 amounts, but that's because they're the 1986 amounts unaltered by inflation. It's intended to replace the $6300 regular amount (c) and 9300 head of household amount (b).
No other mention is made of 26 USC 63 (f).
In the conference report, this is laid out in more detail. The original House bill did exclude this deduction (page 14 of the discussion of the joint report, page 537 overall of the full conference report):
The provision eliminates the additional standard deduction for the aged and the blind.
While the Senate bill did not (page 15/538):
The additional standard deduction for the elderly and the blind is not changed by the provision.
In the Conference Agreement, the Senate version was accepted:
The conference agreement follows the Senate amendment.
Thus, as of the conference report, and specifically clarified in the discussion below the conference version of the bill, the extra deduction was preserved for the elderly or blind. When the final amended text of 26 USC 63 is available, this answer should be edited to include the final details.