Corpus Christi is, of course, a feast day – a single day, hence it is not appropriate to use its collect for the days following, just as you would not use the collect of the Day of Pentecost for the days following, nor the collect for Trinity Sunday for the days following.
Common Worship (CofE) has this collect/opening prayer for the First Sunday after Trinity, and hence the week following.
BCP (TEC) has the following collect for the week following Sunday June 6:
from whom all good proceeds:
Grant that by your inspiration we may think those things that are right,
and by your merciful guiding may do them;
through Jesus Christ our Lord,
who lives and reigns with you and the Holy Spirit,
one God, for ever and ever. Amen.
The Anglican Church in Aotearoa, New Zealand and Polynesia (ACANZP) has the second Sunday after Pentecost as Te Pouhere Sunday, “Designated by General Synod to celebrate our life as a three Tikanga Church”. This has its own readings etc. The lectionary states “Resources are available on the General Synod website” and how to find them. That may have been true at the printing of this lectionary, but the resources are no longer there. The Dunedin diocesan site has possibly the best of NZ’s liturgical resources available, but even there the links appear broken. I think it possible that this is the document that used to be on the General Synod site, that the lectionary is referring to. Someone has told me that ACANZP has 38 special Sundays during the 52 week year – I can almost believe it. This is one of these 38.
Please in the comments feel free to add hymns, prayers, resources, etc. for Corpus Christi etc.