You have the gist of almost all of this (disregarding the Latin endings), which is no mean feat, given all the 'etc.' and abbreviations.
But the issue is that Mary Read didn’t name an executor, which is why administration was granted to Roger Philpott, with the will annexed. To be fair, the word ‘executor’ doesn’t actually appear, but it can be inferred from the phrase nullum … no(m)inavit aut constituit &c (‘named no-one, nor constituted etc.’).
I would question whether the surname of the 3rd Mary is Primor (line 3, as you have it), unless perhaps you have this name from the will itself? But I'm not fully convinced by Pamor either. It could be Pavior, but there is no dot for the i, and this clerk does generally seem to dot his i's, albeit with much displacement to the right.
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21 Junij 1664 Coram m(agist)ro Will(el)mo Lovelace
Cl(er)ico sub(stitu)to &c p(rese)nte me Paulo Lukin no(tar)io
pub(li)co
Probat(um) fuit test(ament)um hu(ius)mod(i) &c Juram(en)tis tam
Marić Wastell Marić Witherden et Marić
Pamor[?] testium &c quam Rogeri Philpott
tutoris sive Curat(oris) Hannć Read filić &c hui(us)m(o)d(i)
defunct(ć) Ac inde approbatum et insinuatum
&c Et quia hu(iusm)o(d)i defunct(a) nullum test(ament)i sui
h(uius)mo(d)i no(m)inavit aut constitutit &c rem quominus &c
Ideo d(omi)nus com(m)isit ad(ministracio)nem bonor(um) hu(iusm)o(d)i defunct(ć)
unacum test(ament)o suo hu(iusm)o(d)i annex(ato) p(re)fato Rogero
Philpott tutori d(i)c(t)ć Hannć Read duran(te) eius
minoritate prius iurat(o) ad s(an)c(t)a &c salvo Jure
&c
21 June 1664 before Master William Lovelace, clerk, substitute etc., in the presence of me Paul Lukin, Notary Public.
This will was proved etc. by the oaths both of Mary Wastell, Mary Witherden and Mary Pamor[?], witnesses etc., and also of Roger Philpott, tutor or curator of Hannah Read, daughter etc. of this deceased, and then approved and inserted etc. And because this deceased named no-one [as executor] of this her will, nor constituted etc. the matter, by which the less etc., therefore the Master granted administration of the goods of this deceased, together with this her will annexed, to the aforesaid Roger Philpott, tutor of the said Hannah Read, during her minority, he first being sworn on the Holy etc., saving the right etc.