The question is moot, given that the sentence is basically broken.
It might be easier to understand the structure of the original by comparing it with other versions:
(1). Central bankers will continue to be
as hawkish as it takes to contain inflation.
pronoun referent: dummy "it" = "to contain inflation"
infinitive attachment: As a
real subject, "to contain inflation" is attached to "as it takes" in the
dependent clause. That is, the whole dependent as-clause should be "as it takes to contain inflation", rather than "as it takes".
(2). Central
bankers will continue to be
as hawkish as they get to contain inflation.
pronoun referent: real subject "they" = "central bankers"
infinitive attachment: As an
infinitive of purpose, "to contain inflation" is attached to "as hawkish" in the
main clause. That is, the whole dependent as-clause should be "as they get", rather than "as they get to contain inflation".
Please contrast (2) with (3) below:
(3). Central bankers will continue to be
as hawkish as it gets to contain inflation.

(This must be incorrect.)
As we see here, (3) is a blend of (1) and (2). But it must be grammatically incorrect because, on the one hand, "it" must refer to "to contain inflation" (, and "it" can't refer to "bankers"), as must the "it" in (1), but on the other hand, with the verb "gets", the dependent as-clause, as in (2), must only be "as it gets", thus making "it" unable to refer to "to contain inflation".
(4). Central bankers will continue to be
as hawkish as is necessary to contain inflation.
pronoun referent: -
infinitive attachment: As an
infinitive of purpose, "to contain inflation" is attached to "as is necessary" in the
dependent clause. That is, "to contain inflation" is an infinitive of purpose both in (2) and (4), but it is an adverbial of purpose in the
main clause of (2), while it is so in the
dependent as-clause of (4).
In a nutshell, "as it takes" in (1) might be an idiom, as LB suggested in #7 and #9,
What it takes – to achieve something, for something to happen, etc. – is an idiomatic concept, which can be used in different ways.
Idioms exist to be used in the time-honoured way, not to be altered beyond recognition.
but it might be better
to see it within the whole as-clause "as it takes to contain inflation", not to see it stand-alone. And in turn "as it takes to contain inflation" should have something to do with the construction "It takes X to do Y", as in "It takes
a hawkish central banker to contain inflation".
If the above observation is correct, then "… as hawkish
as it takes to contain inflation" in the OP might be seen as derived from “ … as hawkish
as (however hawkish a central banker) it takes to contain inflation”, though we don't normally say the latter.
What would you say to the above reasoning?