Firstly, quoting the answer of @JohnLawler to lend context to the rest of my answer:
Some indication of a gap in sequence is necessary, but " " is not a conventional sign of it. Three ... periods in a row between quotes " ... " is better. Some use two, but three seems somewhat more conventional. The Unicode "horizontal ellipsis" character … takes up only one space (but should have a space on both sides)
Now, to try and add a bit of value to his answer, and so give this question an answer to tick to render it completed...
Another technique you can use to show a lapse of time, but also a sharp change in location or subject, analogous to a fade to black cut in film is a section break (note, I was taught at school this was termed ekphrasis, but no google result I found supported this, perhaps someone else knows a better term). It is typically indicated by a unique character (depending on writer preference) centred on a line following the end of a paragraph.
With your example sentences it might work something like this:
"I need to read the letter before I can comment."
"It looks like he's determined to come here."
Here the first sentence is said as the last sentence of a paragraph where, for example, a student asks a university admissions tutor about the suitability of their letter as part of an application for graduate school. The ✪ character (minor formatting mishap aside) is used to indicate a passing of time and place, and the second sentence is now the start of a conversation between the university admissions tutor and one of their colleagues, discussing the student, occurring later and possibly in a different place (determined by the subsequent context).